1876.] 



191 



I Chase. 



motion, we obtain, in units of Eartli's mean radius vector, Earth, 1.258; 

 Jupiter, .691)4. Jupiter's proper motion is, therefore, that whicli is due tlie 

 "centre of cxi)losive oscillation," (J), of which Earth is a limit. 



Those accordances furnish new data for approximating to tlie primitive 

 parabolic abscissas of interstellar action. For if we take the kinetic radius 



1.4232 r = radius oi mean velocity of radial, synchronous with 



:■-■ + 4 



with circular, oscillation 



and the solar modulus limit of possible atmos- 



phere, (35.813 X radius) as determinants, the three known abscissas (^; •? 



+ 'J + ''^ + 27^-(" '''29 ^) gi^6 the following logarithms for planetary 

 and stellar abscissas: 



Theoreti- Perihe- 



^ = solar radius 



e + ry + C ^ 1.42324* 



cal. 

 .000000 



.114950 



lion. 



Aphe- 

 lion, 



f © 

 Id" 

 I Asteroid 



6 

 7 



log. 



'-h 



IS 



35.813 Mf 

 a CentauriX 



Mean. 

 .000000 

 .114950 

 c + 10 >? -f 100 C = 1.678467 1.680602 1.795038 1.885522 

 c -f 11 ^5 -f 121 C = 1.910966 1.858650 1.890463 1.920003 

 I 4- 12 ij -f 144 C = 2.155219 2.125604 2.156064 2.184527 

 c + 13 >? -f 169 C" r= 2.411227 2.324836 2.390112 2.446847 

 ? + 14 'J + 196 C = 2.678989 



? + 15 5? 4- 225 r = 2.958507 2.941956 2.969211 2.994855 



1^ _|_ 16 ij + 256 C = 3.249779 3.206444 3.244704 3.279865 



c + 17 5? + 289 : = 3.552807 3.521682 3.557093 3.589694 



1^ -|_ 18 ij + 324 C == 3.867589 3.861415 3.867758 3.873951 



4^ _|_ 27 >? -f 729 ? = 7.229595 7.229595 



c -f 28 >? + 784 C = 7.661925 7.657096 7.686009 



We have seen (5) that the limits of the planetary system (Mercury and 



Neptune), were fixed by the radius of internal rupture and the nucleal 



radius which correspond to the modulus of light. The values ^, f, |, &c., 



represent the points at which particles falling from !?•, 2r, 3?-, &c., would 



acquire the velocity of central disintegration (|/2gr). The like co-efficients 

 of Mercury and Mars (f ) seem to indicate satellite relations to Earth and 

 Venus ; all the abscissas between Mercury and Neptune, are within the 

 range of orbital eccentricities, the greatest deviations of the theoretical from 

 the mean values being those of Venus and Mars, which are less than five 



* The nucleal radius varying as the % power of the atmospheric radius. Com- 

 pare Alexander's ratio for exterior half-planets {Smithsonion Contributions, 280, 

 p. 5.) 



t Modulus, or the double height of virtual fall which would give the velocity 

 of light, bearing the same ratio to the modular atmosphere, as solar radius 

 bears to solar atmosphere. 



X The least value is given by Norton; the greatest by Denison. There is no 

 reason for doubting that the true value is between the two; 



